Rewriting reduction and pruning reduction on Munn trees

We introduce the processes of rewriting reduction and pruning reduction on Munn trees (finite birooted trees with labelled edges) and use them to develop a general strategy to solve the idempotent word problem for inverse monoid presentations. The process of rewriting reduction on Munn trees is a generalization of the standard processes of rewriting on strings that is widely studied in computer science. The process of pruning reduction is a geometric adaptation of the process of rewriting reduction on Munn trees and is introduced as a natural way to deal with Munn trees, which may be viewed as two dimensional structures. The main part of the dissertation is devoted to a class of inverse monoid presentations of the form...